Let z be a complex number such that
z + 1/z = 1
Find
z^3
Squaring both sides of the equation z+1/z=1, we get [z^2 + 2 + \frac{1}{z^2} = 1,]so z2+1/z2=−1. Then (z+1/z)(z2+1/z2)=(z+1/z)(−1)=−1, so z3+1=−1, so z3=−2.
